Hydrocarbon reservoirs are porous bodies of rock in the subsurface where the pore spaces within the rock are at least partly filled by hydrocarbons. Reservoir rocks are typically sedimentary rocks composed of several different classes of inclusions and voids. For example, in a siliciclastic rock, the compositional classes might be large quartz grains, small quartz grains, feldspar grains, calcite cement which binds the grains together, clay, and pore space between the grains. In a carbonate rock, the compositional classes might be shell fragments, skeletal remains, microporous regions, vugs, and intergranular pores. Within a single geologic formation or stratigraphic unit, rocks will typically contain the same compositional classes, though the volume fractions of each class may vary. Based on the geologic context of a new prospect, geologists can often predict the compositional classes that will be found in a prospective reservoir, though the volume fractions of each compositional class at a given location within the reservoir are typically unknown before drilling.
Since rocks within a single formation typically have the same compositional classes and similar pore-scale structure, rock samples from one location can often be used to predict relationships between properties at a different location in the same formation where a sample is not available. Rock samples from an analog formation, a different formation thought to have similar structure and composition, can also be used to predict relationships between properties in a formation of interest.
The composition and structure of a reservoir rock and the type of fluid in the pore space of the rock influence the reflection and transmission of seismic waves by the rock and the conductivity and dielectric constant of the rock. Relationships among seismic, electrical and reservoir properties are exploited in geophysical prospecting for hydrocarbons, where data from seismic or electromagnetic surveys are used to predict the spatially-varying properties of a reservoir. The predicted reservoir properties are the basis for decisions about how many wells to drill, the type of well to drill, and where the wells should be placed to optimally recover the resource from the reservoir.
Seismic properties of a reservoir rock are those properties that directly determine the reflection and transmission of seismic waves by the rock, and together define at least the compressional wave velocity, shear wave velocity, and density of the rock. It is often more convenient to express the seismic properties of a rock in terms of elastic properties, such as bulk modulus and shear modulus (also called the elastic moduli). Various functions of the velocities and density of the rock can be equivalently used to express seismic properties, including: bulk modulus, shear modulus, Poisson's ratio, Vp/Vs ratio, P-wave modulus, and Lamé parameters. Seismic properties may also include, for example, anisotropy and attenuation. Seismic wave velocities may vary with the frequency of the seismic wave, a phenomenon called dispersion. Among the seismic properties, density is a simple function of the volume fractions of compositional classes, being the volume-weighted average of the densities for each compositional class independent of the structure of the rock. By contrast, the relationship between elastic properties and volume fractions is complicated and will vary between different formations due to variations in structure.
Electrical properties of a reservoir rock are those that determine the electrical current that results from an applied electrical potential, and include at least the conductivity or resistivity of the rock. Electrical properties may also include, for example, the capacitance or dielectric constant of a reservoir rock, the frequency dependence of conductivity and dielectric constant, as well as anisotropy parameters associated with directional variation in conductivity and capacitance. Sometimes the effect of the rock matrix on conductivity is expressed by the formation factor, which is the ratio of the conductivity of the pore fluid to the conductivity of the fluid-saturated rock. The relationship between electrical properties and the volume fractions of the compositional classes in a rock is complicated and formation dependent since electrical properties also depend on structure.
Reservoir properties include the composition, pore-scale structure or texture, and pore fluid contents of the reservoir rock as it varies throughout the reservoir. Of direct importance to hydrocarbon production is the type of pore fluid and the porosity and permeability of the reservoir rock. The pore fluid type is oil, natural gas, ground water, or some combination of those. The porosity determines the volume of fluid in the reservoir. Often it is important to further distinguish between connected porosity which can be drained through a nearby well and unconnected porosity which cannot be drained at economically significant rates but may play a role over geologic time in determining the distribution of fluids in the reservoir. The permeability and its spatial distribution within the reservoir determine whether the fluid may be produced from the reservoir at an economically viable rate. Variability in the mineral composition and pore geometries of the reservoir rock can mask the effect of fluid type, porosity, and permeability on seismic and electrical properties. Thus accurate quantification of composition and pore geometries may also be necessary in order to determine pore fluid type, porosity, and permeability. Many reservoir properties may be directly expressed by the volume fractions of appropriately defined compositional classes in the reservoir rock. For example, porosity is simply the volume fraction of pore space, and mineral composition is given as the volume fraction of each mineral type, usually divided by the total mineral (non-pore) volume fraction. Pore fluid type may be directly expressed by volume fractions of water, oil, and gas within the pore space, and grain size distributions are expressed by the volume fractions of grains falling into each of several size ranges. By contrast, permeability depends on rock structure as well as the volume fractions of compositional classes. The relationship between permeability and the volume fractions of compositional classes that applies for one formation may not apply in a different formation with the same compositional classes due to differences in rock structure.
It is important to distinguish between the local properties at points within a rock sample and the effective medium (sometimes called bulk) properties of the sample taken as a whole. For example, a seismic wave velocity can be specified for the mineral or pore fluid at each point within the sample. However, seismic waves of interest have wavelengths much longer than the diameter of any grain or pore within the sample so they travel through the sample at an intermediate “effective” or “bulk” velocity which is a complicated average over the velocities of the compositional classes that make up the sample.
Relationships among seismic, electrical, and reservoir properties are used in predicting reservoir properties from geophysical survey data. In current practice, such relationships come from two sources: empirical studies and theoretical models. In empirical studies, rock samples are obtained from a geological analog, a formation thought to have similar properties to the reservoir. The effective properties of these samples are measured in the laboratory, and an empirical curve or surface is fit through the measured values that seems to characterize the relationship between the properties of interest. [e.g., Dvorkin and Nur, 1996] Sometimes down-hole measurements by well logging tools are used in lieu of or in combination with lab measurements to establish empirical relationships. [e.g., Greenberg & Castagna, 1992] The empirical relationship may be a simple curve fit or a more complicated one estimated by artificial neural networks. [Hoskins & Ronen, 1995] The relevance of empirical relationships depends on the extent to which the source of the rock samples resembles the prospective reservoir. The accuracy depends on whether the quantity and quality of the measurements are sufficient to discern the true relationship between the properties of interest. When a large number of properties must be included in the relationship, empirical methods are often unable to resolve their separate contributions.
In certain idealized cases, theoretical models give relationships between properties. For example, if a rock consists of a homogeneous background material with non-interacting spheroidal inclusions of other materials or pores, the relationship between the effective elastic moduli of the rock and the volume fractions of the inclusions can be calculated analytically. A theoretical model is available for this case because the idealized structure of this rock (spheroidal inclusions) is amenable to analytical calculations. This theoretical model is based on the elastic properties of the background material, the elastic properties of the inclusions, and the shape of the inclusions. For spheroidal inclusions, shape is fully characterized by specifying the aspect ratio. A spheroid is a three-dimensional shape formed by rotating an ellipse around one of its two axes, and the aspect ratio of the resulting spheroid is the ratio of the length of the axis of rotation to the length of the other axis of the ellipse. For example, for oblate spheroids, the axis of rotation is the minor axis of the ellipse, and the aspect ratio is less than one. A theoretical model for the elastic properties of a rock with spheroidal inclusions is given by Kuster & Toksöz [1974]. The Kuster-Toksöz (KT) model is only accurate for low concentrations of inclusions, but differential effective medium (DEM) theory teaches that the KT model can be applied with a process of iterative homogenization: adding an inclusion, calculating the effective properties, assuming a new homogeneous background with those properties, and repeating until all inclusions are added. This DEM theory approach provides accurate predictions out to higher volume fractions. An alternative to DEM theory is self-consistent (SC) theory which teaches that when small concentrations of each inclusion type are added (e.g., using KT theory) in correct proportion to a homogeneous background having the correct effective medium properties, then the addition does not change the effective medium properties. Under SC theory, values for background properties are tried until the addition of the inclusions leaves them unaltered. DEM and SC results are available for permeability and conductivity as well as elastic properties. [Torquato, 2002] The accuracy of theoretical models is limited by the extent to which the rocks conform to the assumptions of the model. The pores and inclusions within real rocks are not spheroidal and do not have well-defined aspect ratios, so theoretical models that assume otherwise must be applied with caution.
In practice, rock properties models often incorporate certain principles from theoretical models together with empirically determined parameters. For example, DEM or SC theory defines a certain family of curves relating effective properties of the rock to the volume fractions of each compositional class. The family of curves is parameterized by the aspect ratios of each compositional class. Although the aspect ratios for real inclusions are not well-defined and therefore cannot be calculated directly from rock images, effective aspect ratios may be selected for each compositional class to best fit the family of curves to lab measurements on actual rock samples. The physical constraints imposed by a theoretical model make it possible to determine property relationships from fewer rock samples than would be required in a purely empirical approach. Constraining the free parameters of a theoretical model typically requires at least as many rock samples as there are parameters, and generally many more due to measurement noise and model approximations. When a theoretical model has more than a few unknown parameters, these typically cannot be accurately determined from lab measurements of effective properties alone.
Another approach to determining relationships between seismic, electrical, and reservoir properties is to generate a set of virtual rock samples by simulating the processes by which siliciclastic rocks are formed: sedimentation, compaction, and diagenesis. [Øren & Bakke, 2002] Various seismic and reservoir properties may be computed for the virtual rock samples produced by the simulation and correlations between the properties explored. [Øren, Bakke, & Held, 2006] The limitation of this method is that the simulation may not accurately reproduce the structure and properties of real rocks. This is particularly a concern for carbonate rocks, where the processes of diagenesis are often more complicated than in siliciclastics.
Computational rock physics is the computation rather than laboratory measurement of seismic, electrical, or reservoir properties of a rock based on numerical simulation at the pore scale. In this technique, a 3D image is taken of a rock sample and a 3D digital representation of the rock is created. By assigning properties to the components of the digital rock and using fundamental physical principles, the effective properties of the rock sample can be computed numerically. When a 3D image is not available, a digital rock can be constructed statistically honoring spatial correlations extracted from a 2D image of the rock. [Nur, 2003] Of course, the digital rock can also be entirely computer generated without reference to an actual rock sample, and such a purely synthetic volume can still be useful for evaluating the idealized assumptions of theoretical models. [e.g., Knackstedt et al, 2005] Recent examples of computational rock physics include the computation of permeability from 3D images and statistical reconstructions from 2D images [Arms et al, 2004; Keehm et al, 2001], computation of effective bulk and shear moduli from 3D images [Arms, 2002], and computation of conductivity from 3D images [Spanne et al, 1994]. While computational rock physics can provide a useful substitute for laboratory measurements in difficult-to-measure rocks, it does not go beyond providing information about the particular rock sample that was imaged or digitally constructed. Specifically, it does not specify a relationship between geophysical and reservoir properties that can be applied in hydrocarbon exploration to other rocks of the same formation.
From the foregoing, it can be seen that there is a need in hydrocarbon exploration for a method that can determine relationships among seismic, electrical, and reservoir properties in complicated rocks where current methods cannot isolate the effects of each compositional class. Preferably, such a method should be able to quantify the impact of each of a large number of compositional classes on the effective properties of a rock, even with a limited supply of rock samples. The present invention satisfies this need.